A262952 Expansion of Product_{k>=1} (1 + x^(2*k-1)) * (1 + x^(3*k-1)).

1, 1, 1, 2, 1, 3, 3, 3, 6, 5, 7, 9, 9, 12, 15, 16, 21, 24, 26, 33, 37, 42, 51, 57, 65, 78, 86, 99, 115, 128, 146, 168, 187, 213, 243, 269, 306, 345, 383, 433, 487, 539, 607, 678, 749, 842, 935, 1033, 1157, 1279, 1413, 1575, 1736, 1916, 2127, 2339, 2579, 2853

Offset: 0

Author

Vaclav Kotesovec, Oct 05 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015

Crossrefs

Cf. A000700, A262928, A262953.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(2*k-1)) * (1 + x^(3*k-1)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ 5^(1/4) * exp(Pi*sqrt(5*n/2)/3) / (2^(23/12) * sqrt(3) * n^(3/4)).